Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use LODE-GP instead of plain GP | GP · Bipendulum | mean ODE error: 0.064 -> 5.135e-07 | Helped |
| use LODE-GP instead of plain GP | GP · Heating | mean ODE error: 0.218 -> 0.008 | Helped |
| use LODE-GP instead of plain GP | GP · Three tank | mean ODE error: 0.040 -> 1.360e-05 | Helped |
| use LODE-GP instead of plain GP | GP · Bipendulum | evaluation RMSE: 0.044 -> 0.106 | Hurt |
| use LODE-GP instead of plain GP | GP · Bipendulum | training RMSE: 0.008 -> 0.060 | No clear effect |
| use LODE-GP instead of plain GP | GP · Heating | evaluation RMSE: 0.333 -> 0.170 | Helped |
| use LODE-GP instead of plain GP | GP · Three tank | evaluation RMSE: 0.058 -> 0.078 | Hurt |
| use LODE-GP instead of plain GP | GP · Heating | loss: -1.628 -> -2.089 | Helped |
| use LODE-GP instead of plain GP | GP · Bipendulum | loss: -2.072 -> -1.638 | Hurt |
| learn ODE parameters a and b by hyperparameter training | LODE-GP · Heating | parameter relative error: 2.8% | Helped |
| add 1% noise when learning ODE parameters | LODE-GP · Heating | parameter relative error: 2.8% -> 5.3% | Hurt |
| use LODE-GP compared with symbolic solution | LODE-GP · Bipendulum | median ODE error: 2e−6 vs 1.75e−7 | No clear effect |
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